Entropy Generation in the ICM

1. Entropy Generation in the ICM Michael Balogh University of Durham Institute for ComputationalCosmology University of Durham

2. Collaborators • Mark Voit (STScI -> Michigan) • Richard Bower, Cedric Lacey (Durham) • Greg Bryan (Oxford) • Frazer Pearce, Brendan Hogg (Nottingham)

3. Entropy: A Review Definition of S: DS = D(heat) / T Equation of state: P = Kr5/3 Relationship to S: S = N ln K3/2 + const. Useful Observable: Tne-2/3  K Convective stability: dS/dr > 0 Only radiative cooling can reduceTne-2/3 Only heat input can raiseTne-2/3

4. T200 K200 = mmp (200fbrcr)2/3 Important Entropy Scales Characteristic entropy scale associated with halo mass M200 v2acc Entropy generated by cold, smooth accretion shock Ksm = 3 (4rin)2/3 (Mt)2/3  (d ln M / d ln t)2/3

5. Dimensionless Entropy From Simulations How is entropy generated initially? Expect merger shocks to thermalize energy of accreting clumps But what happens to the density? Voit et al. (2003) Simulations from Bryan & Voit (2001) Halos: 2.5 x 1013 - 3.4 x 1014h-1MSun

6. Smooth vs. Lumpy Accretion SMOOTH LUMPY Smooth accretion produces ~2 times more entropy than hierarchical accretion (but similar profile shape) Voit et al. (2003)

7. (M2-1)2 48/3Ksm M2 5 K1 vin2 3(4r1)2/3 Preheated smooth accretion • If pre-shock entropy K1≈Ksm, gas is no longer pressureless = K2 ≈ Ksm + 0.84K1, for Ksm/K1» 0.25 ≈ + 0.84K1 Note adiabatic heating decreases post-shock entropy

8. 2 1.5 1 0.5 0 K (1034 erg cm2 g-5/3) 0 0.5 1 fg=Mg/fbM200 Preheating and smooth accretion M(to)=1013h-1Mo 2 1.5 1 0.5 0 M(to)=1014h-1Mo Kmod Kmod Ksm Ksm K1 K (1034 erg cm2 g-5/3) K200 K200 Kc(T200) K1 0 0.5 1 fg=Mg/fbM200 Early accretion is isentropic; leads to nearly-isentropic groups Voit et al. 2003

9. Entropy in groups Scaled entropy (1+z)2T-0.66S Scaled entropy (1+z)2T-1S Radius (r200) Radius (r200) Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T0.65 Cores are not isentropic Pratt & Arnaud (2003)

10. Excess Entropy at R500 Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2 Voit & Ponman (2003)

11. Smooth accretion on groups? • Groups are not isentropic, but do match the expectations from smooth accretion models • Relatively small amounts of preheating may eject gas from precursor haloes, effectively smoothing the distribution of accreting gas. • Self-similarity broken because groups accrete mostly smooth gas, while clusters accrete most gas in clumps

12. Lumpy accretion • Assume all gas in haloes with mean density Dfbrcr K(t) ≈ (r1/ Dfbrcr)2/3 Ksm(t) ≈ 0.1 Ksm(t) Two solutions: K vin2/r2/3 1. distribute kinetic energy through turbulence (i.e. at constant density) 2. vsh ≈ 2 vac (i.e. if shock occurs well within R200)

13. Binary merger models Maximum velocity model initial distribution final To double mass, need entropy jump of 1.6. For realistic power spectrum, self-similarity requires 1.59<K2/K1<2

14. Realistic mass spectrum Entropy generation is still insufficient to preserve initial profile. Low density gas highly shocked to greater and greater entropy

15. SPH Simulations • Simulations of galaxy mergers to study entropy generation • 1:1, 1:8 and 1:16 mergers • vary impact parameter, infall velocity • explore effect of preheating

16. 10 Mpc Post-merger remnant 1:8 merger Collision direction Density

17. 10 Mpc Post-merger remnant 1:8 merger Entropy

18. 10 Mpc Post-merger remnant 1:8 merger Entropy change

19. Post-merger Pre-merger Entropy fgas Simulations Even the small merger is able to generate substantial entropy Surprisingly, appears to result in a simple shift to the entropy distribution… by factor of 1.6!

20. Conclusions • Smooth accretion onto groups may explain higher entropy gas in those systems • Lumpy accretion: may be difficult to generate enough entropy through accretion shocks alone • but simulations are encouraging: entropy production appears to be simple